It was in the UK's national interest to join the EU, and encourage it to grow. The reasoning was broadcast thirty-seven years ago in the BBC comedy
Yes, Minister, and remains valid today:
Sir Humphrey Appleby: Minister, Britain has had the same foreign policy objective for at least the last 500 years: to create a disunited Europe. In that cause we have fought with the Dutch against the Spanish, with the Germans against the French, with the French and Italians against the Germans, and with the French against the Germans and Italians. Divide and rule, you see. Why should we change now, when it's worked so well?
James Hacker: That's all ancient history, surely.
Sir Humphrey Appleby: Yes, and current policy. We had to break the whole thing up, so we had to get inside. We tried to break it up from the outside, but that wouldn't work. Now that we're inside we can make a complete pig's breakfast of the whole thing: set the Germans against the French, the French against the Italians, the Italians against the Dutch. The Foreign Office is terribly pleased; it's just like old times.
James Hacker: Surely we're all committed to the European ideal.
Sir Humphrey Appleby: Really, Minister. [laughs]
James Hacker: If not, why are we pushing for an increase in the membership?
Sir Humphrey Appleby: Well, for the same reason. It's just like the United Nations, in fact. The more members it has, the more arguments it can stir up. The more futile and impotent it becomes.
James Hacker: What appalling cynicism.
Sir Humphrey Appleby: Yes. We call it diplomacy, Minister.
Sir Humphrey was cynical, but he wasn't wrong. At least since the time of Elizabeth I, England (and later the UK) intervened in Europe to prevent any one power from growing too strong. It would conduct diplomacy, and fight wars if needed, to constrain strong governments on the Continent. This held true as great powers rose and fell, from Habsburg Spain to Napoleonic France to imperial Germany. In this way the UK was able to promote its own trade, security, and other national interests.